It is the first major company to invoke the looser rules, aimed at creating a more attractive business climate for investors by making it less expensive to hire and fire workers.
PSA will also offer 900 early retirement plans, but said it planned to offset the redundancies by creating 1,300 new jobs with long-term contracts this year and 2,000 apprentices for younger workers.
It said at least half of entry-level positions would be filled "by the group's former interns or work-study employees."
Macron, a former investment banker who is pushing for a "French renaissance", used executive decrees in September to shake up collective bargaining rules, overcoming the resistance of the far left and some labour unions.
Under the new legislation, companies can cut jobs by offering voluntary redundancy packages instead of having to draw up a company-wide restructuring plan, which requires the company to prove it faces financial difficulties.
Knowing that they can lay off workers more easily is intended to entice employers to hire more people in the first place, the theory goes, but critics see Macron's changes as eroding job security and protections.
The goal is to cut a French unemployment rate currently at 9.2 percent, above the euro zone average of 8.7 percent and much higher than the 3.6 percent in neighbouring Germany.
Voluntary redundancies existed before Macron's reforms, but only on a case-by-case basis.
French clothing retailer Pimkie also said this week that it would use the new rules to try to cut 208 jobs out of roughly 1,900 in France.
But PSA, whose brands include Peugeot, Citroen, Opel and Vauxhall, was the first major company to invoke the new rules ahead of a meeting with union leaders Tuesday.
The head of the militant CGT union, which led protests against the reforms in September, accused the company of a race to the bottom.
"The management at PSA wants to turn permanent contracts into unstable jobs, temporary work, etc.," Philippe Martinez told France Info radio.
Head of the militant CGT union, Philippe Martinez. Photo: AFP
Union agreement needed
PSA has to obtain the agreement of unions representing at least 50 percent of workers to proceed with the plan and cannot force workers to take the redundancy package on offer.
But for Martinez, executives now have the upper hand.
"I know that some directors at big companies will say 'It's either this or else I close a factory'," he said. "We all know of a number of cases when volunteers are forced."
In the wake of Tuesday's meeting, the CGT called the plan "unacceptable" at a time when PSA is earning "billions" of euros.
The company posted a net profit of 2.15 billion euros ($2.6 billion) for 2016, an improvement that prompted management to resume paying shareholder dividends for the first time since 2011.
But several other unions gave a cautious backing to the plan.
"This isn't a layoff plan but an offer for voluntary departures" that will help the automaker adapt to a changing market," the CFTC union said in a statement.
The CFDT, meanwhile, said that while it welcomed the hiring plans, it "regretted" that PSA was planning just 400 new permanent contracts in manufacturing, where about 8,000 jobs are held by temporary workers, compared with 200 in R&D and 700 in marketing.